I collected tree ring data from 4 regions across California and performed analyses on detrended growth during drought years where water availability (SPEI) was in the bottom 15th percentile. All tree ring series were spline detrended.
\[ Growth Reduction = \frac{\overline{RWI}_{non-drought} - RWI_{drought}}{\overline{RWI}_{non-drought}} \] \[ Recovery = RWI_{actual} - RWI_{pred} \]
Where \(RWI_{pred}\) is the predicted growth for a tree given the post-drought year conditions based on hierarchical Bayesian models of all growth years.
This approach differs in that here we explore the results of the full expression of the model to answer the above questions i.e. the most complex justifiable model. Each species is modeled independently. This approach is a way to avoid the model selection issues we discussed regarding the complexity of question 3.
\[ Reduction_i \sim Normal(\mu_i, \sigma_i) \]
\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}SPEI_i + \beta_{2region_i}DBH_i + \beta_{3region_i}log(hegyi)_i + \beta_{4}SPEI_i\times DBH_i + \beta_{5}SPEI_i \times log(hegyi)_i \]
and for recovery:
\[ Recovery_i \sim Normal(\mu_i, \sigma_i) \]
\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}Reduction_i + \beta_{2region_i}DBH_i + \beta_{3region_i}log(hegyi)_i + \beta_{4}Reduction_i\times DBH_i + \beta_{5}Reduction_i \times log(hegyi)_i \]
Does it make sense for DBH, comp, and interactions to vary regionally? What does this mean? Regionally varying responses to drought intensity or severity could reflect local adaptation.
\(SPEI \times DBH\) smaller or larger trees experience the same drought intensity differently. Perhaps this is due to differences in evaporative demand, root:shoot allocation patterns, height water relationship
\(Reduction \times DBH\) smaller or larger trees recover from equally damaging droughts differently. Potentially due to access to resources, allocation again.
\(SPEI \times log(hegyi)\) sparse or dense neighborhoods modify the effect of drought intensity. This could be via resource (water) competition. Although because we lack good characterization of the between neighborhood microsite differences density could reflect suitability more than competition.
\(Reduction \times log(hegyi)\) sparse or dense neighborhoods modify the recovery of trees from equally damaging droughts. This could also be via resource competition although more than just water. Again, patterns may reflect uncharacterized microsite differences rather than competition.
All models converged Rhat ~1 and each model had few divergent samples. Param estimates and plots were prepared with tidybayes. Marginal effects plots were produced with add_fitted_draws() setting re_formula = ~(spei12 + DBH + comp | Region)) excluding (1 | tree.uniqueID).
| waic_diff | se | |
|---|---|---|
| SPEI only | 0.00000 | 0.000000 |
| Species + SPEI | 2.04252 | 3.076878 |
| Species * SPEI | 4.74648 | 3.720620 |
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| PJ - AC > 0 | 0.0666103 | 0.0096405 | 0.0505275 | 0.0820601 | Inf | 1.0000 |
|
| PL - AC > 0 | 0.0342796 | 0.0118112 | 0.0155830 | 0.0540833 | 9.9900e+02 | 0.9990 |
|
| PL - PJ > 0 | -0.1272120 | 0.0475280 | -0.2065795 | -0.0489364 | 5.5304e-03 | 0.0055 |
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| PJ - AC > 0 | 0.0205816 | 0.0136596 | -0.0024442 | 0.0429330 | 14.094340 | 0.93375 | |
| PL - AC > 0 | 0.0103469 | 0.0157787 | -0.0155560 | 0.0364456 | 2.906250 | 0.74400 | |
| PL - PJ > 0 | -0.0102347 | 0.0161652 | -0.0368797 | 0.0164271 | 0.356392 | 0.26275 |
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.000000 | 0.00000 |
| Varying intercept | 4.186948 | 10.25373 |
| No species effect | 12.834264 | 12.04065 |
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| PJ - AC > 0 | 0.0551883 | 0.0086157 | 0.0409969 | 0.0693746 | Inf | 1.00000 |
|
| PL - AC > 0 | 0.0358049 | 0.0107017 | 0.0183191 | 0.0538784 | 3.99900e+03 | 0.99975 |
|
| PL - PJ > 0 | -0.0891320 | 0.0502752 | -0.1715589 | -0.0051960 | 4.32968e-02 | 0.04150 |
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| PJ - AC > 0 | 0.0315932 | 0.0175444 | 0.0029861 | 0.0603802 | 27.98551 | 0.96550 |
|
| PL - AC > 0 | 0.0967908 | 0.0224670 | 0.0598268 | 0.1338717 | Inf | 1.00000 |
|
| PL - PJ > 0 | 0.0651976 | 0.0225358 | 0.0287279 | 0.1016507 | 1332.33333 | 0.99925 |
|
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| PJ - AC > 0 | -0.0809188 | 0.0411304 | -0.1481597 | -0.0133473 | 0.025641 | 0.02500 | |
| PL - AC > 0 | 0.0800334 | 0.0534826 | -0.0074203 | 0.1685892 | 14.094340 | 0.93375 | |
| PL - PJ > 0 | 0.1609522 | 0.0511764 | 0.0771802 | 0.2447245 | 1332.333333 | 0.99925 |
|
Regional differences are crucial to dtermining growth reduction. Across all species at least two sites are significantly different from one another in intercept and spei slope. The site patterns across species are qualitatively consistent which is in line with the model selection supporting modeling all of the species together.
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.00000 | 0.00000 |
| No regional effects | 43.30953 | 12.80732 |
| Varying intercept | 45.11601 | 12.72891 |
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.00000 | 0.00000 |
| Varying intercept | 41.83552 | 12.88420 |
| No regional effects | 43.82051 | 13.91644 |
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.00000 | 0.000000 |
| No regional effects | 18.41681 | 7.836080 |
| Varying intercept | 19.29546 | 7.449942 |
Regional effects appear to be less important for recovery as none of the intercepts growth reduction slopes for any sites are significantly different from one another. Note that these results differ from the simpler model as the CI are wider here (see other md).
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.000000 | 0.000000 |
| Varying intercept | 1.851447 | 5.964911 |
| No regional effects | 12.912958 | 9.351119 |
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.000000 | 0.000000 |
| Varying intercept | 7.988191 | 8.352711 |
| No regional effects | 22.441717 | 12.987328 |
| waic_diff | se | |
|---|---|---|
| Varying intercept and slope | 0.000000 | 0.000000 |
| Varying intercept | 4.836886 | 8.154183 |
| No regional effects | 36.244175 | 11.872226 |
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| region intercept/total | 0.5970135 | 0.1336668 | 0.3013006 | 0.8868626 | NA | NA |
|
| region slope/total | 0.2677814 | 0.1137323 | 0.0737678 | 0.5785439 | NA | NA |
|
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| region intercept/total | 0.5486569 | 0.1608815 | 0.2163339 | 0.8879885 | NA | NA |
|
| region slope/total | 0.2554130 | 0.1337445 | 0.0574560 | 0.6456691 | NA | NA |
|
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| region intercept/total | 0.4047434 | 0.3123458 | 0.0035201 | 0.9735754 | NA | NA |
|
| region slope/total | 0.4766134 | 0.3515581 | 0.0141206 | 0.9946826 | NA | NA |
|
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| region intercept/total | 0.2333188 | 0.2132561 | 0.0152736 | 0.8137307 | NA | NA |
|
| region slope/total | 0.3221096 | 0.2583555 | 0.0039577 | 0.8943126 | NA | NA |
|
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| region intercept/total | 0.1958702 | 0.2089063 | 0.0081197 | 0.8032205 | NA | NA |
|
| region slope/total | 0.3258525 | 0.2541065 | 0.0158146 | 0.9298125 | NA | NA |
|
| Hypothesis | Estimate | Est.Error | CI.Lower | CI.Upper | Evid.Ratio | Post.Prob | Star |
|---|---|---|---|---|---|---|---|
| region intercept/total | 0.2531975 | 0.2850897 | 0.0014873 | 0.9548398 | NA | NA |
|
| region slope/total | 0.5320250 | 0.3267092 | 0.0123234 | 0.9933452 | NA | NA |
|
Median and 95% CI growth reduction regression coefficients for a) white fir, b) jeffrey pine, and c) sugar pine as well as recovery regression coefficients for d) white fir, e) jeffrey pine, and f) sugar pine.
DBH, competition and their interaction with spei are surprisingly of little effect with the exception of the importance of DBH and its interaction with spei for Jeffrey pine where larger trees fare worse in more severe droughts.
Keep in mind that in the scatter plots the drought intensity axis is flipped, so slope will appear to be wrong sign from the parameter estimate plots.
Recovery shows some evidence that tree and stand characteristics are important to the overall drought response. White fir recovery is impacted by DBH, although this does not vary dramatically region to region. Recovery in two out of four populations of jeffrey pine are affected by competition through the interaction with growth reduction. In these locations recovery from episodes that result in growth reductions is better in dense areas and worse in areas with lower competition (potential microsite signal as mentioned earlier). Sugar pine in the two southern regions appears to be dependent on DBH and competition; larger trees and trees in more dense neighborhoods have better recovery.